----------------------------------------------------------------------------- -- | -- Module : Data.SBV.Provers.Prover -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- -- Provable abstraction and the connection to SMT solvers ----------------------------------------------------------------------------- {-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE NamedFieldPuns #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeSynonymInstances #-} module Data.SBV.Provers.Prover ( SMTSolver(..), SMTConfig(..), Predicate, Provable(..), Goal , ThmResult(..), SatResult(..), AllSatResult(..), SafeResult(..), OptimizeResult(..), SMTResult(..) , SExecutable(..), isSafe , runSMT, runSMTWith , SatModel(..), Modelable(..), displayModels, extractModels , getModelDictionaries, getModelValues, getModelUninterpretedValues , boolector, cvc4, yices, z3, mathSAT, abc, defaultSMTCfg ) where import Control.Monad (when, unless) import Control.DeepSeq (rnf, NFData(..)) import Control.Concurrent.Async (async, waitAny, asyncThreadId, Async) import Control.Exception (finally, throwTo, AsyncException(ThreadKilled)) import System.IO.Unsafe (unsafeInterleaveIO) -- only used safely! import System.Directory (getCurrentDirectory) import Data.Time (getZonedTime, NominalDiffTime, UTCTime, getCurrentTime, diffUTCTime) import Data.List (intercalate, isPrefixOf) import Data.SBV.Core.Data import Data.SBV.Core.Symbolic import Data.SBV.SMT.SMT import Data.SBV.Utils.TDiff import qualified Data.SBV.Control as Control import qualified Data.SBV.Control.Query as Control import qualified Data.SBV.Control.Utils as Control import GHC.Stack import qualified Data.SBV.Provers.Boolector as Boolector import qualified Data.SBV.Provers.CVC4 as CVC4 import qualified Data.SBV.Provers.Yices as Yices import qualified Data.SBV.Provers.Z3 as Z3 import qualified Data.SBV.Provers.MathSAT as MathSAT import qualified Data.SBV.Provers.ABC as ABC mkConfig :: SMTSolver -> SMTLibVersion -> [Control.SMTOption] -> SMTConfig mkConfig s smtVersion startOpts = SMTConfig { verbose = False , timing = NoTiming , printBase = 10 , printRealPrec = 16 , transcript = Nothing , solver = s , smtLibVersion = smtVersion , satCmd = "(check-sat)" , allSatMaxModelCount = Nothing -- i.e., return all satisfying models , isNonModelVar = const False -- i.e., everything is a model-variable by default , roundingMode = RoundNearestTiesToEven , solverSetOptions = startOpts , ignoreExitCode = False , redirectVerbose = Nothing } -- | If supported, this makes all output go to stdout, which works better with SBV -- Alas, not all solvers support it.. allOnStdOut :: Control.SMTOption allOnStdOut = Control.OptionKeyword ":diagnostic-output-channel" [show "stdout"] -- | Default configuration for the Boolector SMT solver boolector :: SMTConfig boolector = mkConfig Boolector.boolector SMTLib2 [] -- | Default configuration for the CVC4 SMT Solver. cvc4 :: SMTConfig cvc4 = mkConfig CVC4.cvc4 SMTLib2 [allOnStdOut] -- | Default configuration for the Yices SMT Solver. yices :: SMTConfig yices = mkConfig Yices.yices SMTLib2 [] -- | Default configuration for the Z3 SMT solver z3 :: SMTConfig z3 = mkConfig Z3.z3 SMTLib2 [ Control.OptionKeyword ":smtlib2_compliant" ["true"] , allOnStdOut ] -- | Default configuration for the MathSAT SMT solver mathSAT :: SMTConfig mathSAT = mkConfig MathSAT.mathSAT SMTLib2 [allOnStdOut] -- | Default configuration for the ABC synthesis and verification tool. abc :: SMTConfig abc = mkConfig ABC.abc SMTLib2 [allOnStdOut] -- | The default solver used by SBV. This is currently set to z3. defaultSMTCfg :: SMTConfig defaultSMTCfg = z3 -- | A predicate is a symbolic program that returns a (symbolic) boolean value. For all intents and -- purposes, it can be treated as an n-ary function from symbolic-values to a boolean. The 'Symbolic' -- monad captures the underlying representation, and can/should be ignored by the users of the library, -- unless you are building further utilities on top of SBV itself. Instead, simply use the 'Predicate' -- type when necessary. type Predicate = Symbolic SBool -- | A goal is a symbolic program that returns no values. The idea is that the constraints/min-max -- goals will serve as appropriate directives for sat/prove calls. type Goal = Symbolic () -- | A type @a@ is provable if we can turn it into a predicate. -- Note that a predicate can be made from a curried function of arbitrary arity, where -- each element is either a symbolic type or up-to a 7-tuple of symbolic-types. So -- predicates can be constructed from almost arbitrary Haskell functions that have arbitrary -- shapes. (See the instance declarations below.) class Provable a where -- | Turns a value into a universally quantified predicate, internally naming the inputs. -- In this case the sbv library will use names of the form @s1, s2@, etc. to name these variables -- Example: -- -- > forAll_ $ \(x::SWord8) y -> x `shiftL` 2 .== y -- -- is a predicate with two arguments, captured using an ordinary Haskell function. Internally, -- @x@ will be named @s0@ and @y@ will be named @s1@. forAll_ :: a -> Predicate -- | Turns a value into a predicate, allowing users to provide names for the inputs. -- If the user does not provide enough number of names for the variables, the remaining ones -- will be internally generated. Note that the names are only used for printing models and has no -- other significance; in particular, we do not check that they are unique. Example: -- -- > forAll ["x", "y"] $ \(x::SWord8) y -> x `shiftL` 2 .== y -- -- This is the same as above, except the variables will be named @x@ and @y@ respectively, -- simplifying the counter-examples when they are printed. forAll :: [String] -> a -> Predicate -- | Turns a value into an existentially quantified predicate. (Indeed, 'exists' would have been -- a better choice here for the name, but alas it's already taken.) forSome_ :: a -> Predicate -- | Version of 'forSome' that allows user defined names. forSome :: [String] -> a -> Predicate -- | Prove a predicate, using the default solver. prove :: a -> IO ThmResult prove = proveWith defaultSMTCfg -- | Prove the predicate using the given SMT-solver. proveWith :: SMTConfig -> a -> IO ThmResult proveWith = runWithQuery False $ ThmResult <$> Control.getSMTResult -- | Find a satisfying assignment for a predicate, using the default solver. sat :: a -> IO SatResult sat = satWith defaultSMTCfg -- | Find a satisfying assignment using the given SMT-solver. satWith :: SMTConfig -> a -> IO SatResult satWith = runWithQuery True $ SatResult <$> Control.getSMTResult -- | Find all satisfying assignments, using the default solver. See 'allSatWith' for details. allSat :: a -> IO AllSatResult allSat = allSatWith defaultSMTCfg -- | Return all satisfying assignments for a predicate, equivalent to @'allSatWith' 'defaultSMTCfg'@. -- Note that this call will block until all satisfying assignments are found. If you have a problem -- with infinitely many satisfying models (consider 'SInteger') or a very large number of them, you -- might have to wait for a long time. To avoid such cases, use the 'allSatMaxModelCount' parameter -- in the configuration. -- -- NB. Uninterpreted constant/function values and counter-examples for array values are ignored for -- the purposes of @'allSat'@. That is, only the satisfying assignments modulo uninterpreted functions and -- array inputs will be returned. This is due to the limitation of not having a robust means of getting a -- function counter-example back from the SMT solver. -- Find all satisfying assignments using the given SMT-solver allSatWith :: SMTConfig -> a -> IO AllSatResult allSatWith = runWithQuery True $ AllSatResult <$> Control.getAllSatResult -- | Optimize a given collection of `Objective`s optimize :: OptimizeStyle -> a -> IO OptimizeResult optimize = optimizeWith defaultSMTCfg -- | Optimizes the objectives using the given SMT-solver. optimizeWith :: SMTConfig -> OptimizeStyle -> a -> IO OptimizeResult optimizeWith config style = runWithQuery True opt config where opt = do objectives <- Control.getObjectives qinps <- Control.getQuantifiedInputs when (null objectives) $ error $ unlines [ "" , "*** Data.SBV: Unsupported call to optimize when no objectives are present." , "*** Use \"sat\" for plain satisfaction" ] unless (supportsOptimization (capabilities (solver config))) $ error $ unlines [ "" , "*** Data.SBV: The backend solver " ++ show (name (solver config)) ++ "does not support optimization goals." , "*** Please use a solver that has support, such as z3" ] let needsUniversalOpt = let universals = [s | (ALL, (s, _)) <- qinps] check (x, y) nm = [nm | any (`elem` universals) [x, y]] isUniversal (Maximize nm xy) = check xy nm isUniversal (Minimize nm xy) = check xy nm isUniversal (AssertSoft nm xy _) = check xy nm in concatMap isUniversal objectives unless (null needsUniversalOpt) $ error $ unlines [ "" , "*** Data.SBV: Problem needs optimization of universally quantified metric(s):" , "***" , "*** " ++ unwords needsUniversalOpt , "***" , "*** Optimization is only meaningful existentially quantified values." ] let optimizerDirectives = concatMap minmax objectives ++ priority style where mkEq (x, y) = "(assert (= " ++ show x ++ " " ++ show y ++ "))" minmax (Minimize _ xy@(_, v)) = [mkEq xy, "(minimize " ++ show v ++ ")"] minmax (Maximize _ xy@(_, v)) = [mkEq xy, "(maximize " ++ show v ++ ")"] minmax (AssertSoft nm xy@(_, v) mbp) = [mkEq xy, "(assert-soft " ++ show v ++ penalize mbp ++ ")"] where penalize DefaultPenalty = "" penalize (Penalty w mbGrp) | w <= 0 = error $ unlines [ "SBV.AssertSoft: Goal " ++ show nm ++ " is assigned a non-positive penalty: " ++ shw , "All soft goals must have > 0 penalties associated." ] | True = " :weight " ++ shw ++ maybe "" group mbGrp where shw = show (fromRational w :: Double) group g = " :id " ++ g priority Lexicographic = [] -- default, no option needed priority Independent = ["(set-option :opt.priority box)"] priority (Pareto _) = ["(set-option :opt.priority pareto)"] mapM_ (Control.send True) optimizerDirectives case style of Lexicographic -> LexicographicResult <$> Control.getLexicographicOptResults Independent -> IndependentResult <$> Control.getIndependentOptResults (map objectiveName objectives) Pareto mbN -> ParetoResult <$> Control.getParetoOptResults mbN -- | Check if the constraints given are consistent, using the default solver. isVacuous :: a -> IO Bool isVacuous = isVacuousWith defaultSMTCfg -- | Determine if the constraints are vacuous using the given SMT-solver. isVacuousWith :: SMTConfig -> a -> IO Bool isVacuousWith cfg a = -- NB. Can't call runWithQuery since last constraint would become the implication! fst <$> runSymbolic (SMTMode ISetup True cfg) (forSome_ a >> Control.query check) where check = do cs <- Control.checkSat case cs of Control.Unsat -> return True Control.Sat -> return False Control.Unk -> error "SBV: isVacuous: Solver returned unknown!" -- | Checks theoremhood using the default solver. isTheorem :: a -> IO Bool isTheorem = isTheoremWith defaultSMTCfg -- | Check whether a given property is a theorem. isTheoremWith :: SMTConfig -> a -> IO Bool isTheoremWith cfg p = do r <- proveWith cfg p case r of ThmResult Unsatisfiable{} -> return True ThmResult Satisfiable{} -> return False _ -> error $ "SBV.isTheorem: Received:\n" ++ show r -- | Checks satisfiability using the default solver. isSatisfiable :: a -> IO Bool isSatisfiable = isSatisfiableWith defaultSMTCfg -- | Check whether a given property is satisfiable. isSatisfiableWith :: SMTConfig -> a -> IO Bool isSatisfiableWith cfg p = do r <- satWith cfg p case r of SatResult Satisfiable{} -> return True SatResult Unsatisfiable{} -> return False _ -> error $ "SBV.isSatisfiable: Received: " ++ show r -- | Prove a property with multiple solvers, running them in separate threads. The -- results will be returned in the order produced. proveWithAll :: [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, ThmResult)] proveWithAll = (`sbvWithAll` proveWith) -- | Prove a property with multiple solvers, running them in separate threads. Only -- the result of the first one to finish will be returned, remaining threads will be killed. -- Note that we send a @ThreadKilled@ to the losing processes, but we do *not* actually wait for them -- to finish. In rare cases this can lead to zombie processes. In previous experiments, we found -- that some processes take their time to terminate. So, this solution favors quick turnaround. proveWithAny :: [SMTConfig] -> a -> IO (Solver, NominalDiffTime, ThmResult) proveWithAny = (`sbvWithAny` proveWith) -- | Find a satisfying assignment to a property with multiple solvers, running them in separate threads. The -- results will be returned in the order produced. satWithAll :: [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, SatResult)] satWithAll = (`sbvWithAll` satWith) -- | Find a satisfying assignment to a property with multiple solvers, running them in separate threads. Only -- the result of the first one to finish will be returned, remaining threads will be killed. -- Note that we send a @ThreadKilled@ to the losing processes, but we do *not* actually wait for them -- to finish. In rare cases this can lead to zombie processes. In previous experiments, we found -- that some processes take their time to terminate. So, this solution favors quick turnaround. satWithAny :: [SMTConfig] -> a -> IO (Solver, NominalDiffTime, SatResult) satWithAny = (`sbvWithAny` satWith) -- | Create an SMT-Lib2 benchmark. The 'Bool' argument controls whether this is a SAT instance, i.e., -- translate the query directly, or a PROVE instance, i.e., translate the negated query. generateSMTBenchmark :: Bool -> a -> IO String generateSMTBenchmark isSat a = do t <- getZonedTime let comments = ["Automatically created by SBV on " ++ show t] cfg = defaultSMTCfg { smtLibVersion = SMTLib2 } (_, res) <- runSymbolic (SMTMode ISetup isSat cfg) $ (if isSat then forSome_ else forAll_) a >>= output let SMTProblem{smtLibPgm} = Control.runProofOn cfg isSat comments res out = show (smtLibPgm cfg) return $ out ++ "\n(check-sat)\n" instance Provable Predicate where forAll_ = id forAll [] = id forAll xs = error $ "SBV.forAll: Extra unmapped name(s) in predicate construction: " ++ intercalate ", " xs forSome_ = id forSome [] = id forSome xs = error $ "SBV.forSome: Extra unmapped name(s) in predicate construction: " ++ intercalate ", " xs instance Provable SBool where forAll_ = return forAll _ = return forSome_ = return forSome _ = return {- -- The following works, but it lets us write properties that -- are not useful.. Such as: prove $ \x y -> (x::SInt8) == y -- Running that will throw an exception since Haskell's equality -- is not be supported by symbolic things. (Needs .==). instance Provable Bool where forAll_ x = forAll_ (if x then true else false :: SBool) forAll s x = forAll s (if x then true else false :: SBool) forSome_ x = forSome_ (if x then true else false :: SBool) forSome s x = forSome s (if x then true else false :: SBool) -} -- Functions instance (SymWord a, Provable p) => Provable (SBV a -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ k a forAll (s:ss) k = forall s >>= \a -> forAll ss $ k a forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ k a forSome (s:ss) k = exists s >>= \a -> forSome ss $ k a forSome [] k = forSome_ k -- SFunArrays (memory, functional representation), only supported universally for the time being instance (HasKind a, HasKind b, Provable p) => Provable (SArray a b -> p) where forAll_ k = declNewSArray (\t -> "array_" ++ show t) >>= \a -> forAll_ $ k a forAll (s:ss) k = declNewSArray (const s) >>= \a -> forAll ss $ k a forAll [] k = forAll_ k forSome_ _ = error "SBV.forSome: Existential arrays are not currently supported." forSome _ _ = error "SBV.forSome: Existential arrays are not currently supported." -- SArrays (memory, SMT-Lib notion of arrays), only supported universally for the time being instance (HasKind a, HasKind b, Provable p) => Provable (SFunArray a b -> p) where forAll_ k = declNewSFunArray Nothing >>= \a -> forAll_ $ k a forAll (_:ss) k = declNewSFunArray Nothing >>= \a -> forAll ss $ k a forAll [] k = forAll_ k forSome_ _ = error "SBV.forSome: Existential arrays are not currently supported." forSome _ _ = error "SBV.forSome: Existential arrays are not currently supported." -- 2 Tuple instance (SymWord a, SymWord b, Provable p) => Provable ((SBV a, SBV b) -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ \b -> k (a, b) forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b -> k (a, b) forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ \b -> k (a, b) forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b -> k (a, b) forSome [] k = forSome_ k -- 3 Tuple instance (SymWord a, SymWord b, SymWord c, Provable p) => Provable ((SBV a, SBV b, SBV c) -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ \b c -> k (a, b, c) forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c -> k (a, b, c) forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ \b c -> k (a, b, c) forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c -> k (a, b, c) forSome [] k = forSome_ k -- 4 Tuple instance (SymWord a, SymWord b, SymWord c, SymWord d, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d) -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ \b c d -> k (a, b, c, d) forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d -> k (a, b, c, d) forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ \b c d -> k (a, b, c, d) forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d -> k (a, b, c, d) forSome [] k = forSome_ k -- 5 Tuple instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ \b c d e -> k (a, b, c, d, e) forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d e -> k (a, b, c, d, e) forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ \b c d e -> k (a, b, c, d, e) forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d e -> k (a, b, c, d, e) forSome [] k = forSome_ k -- 6 Tuple instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SymWord f, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ \b c d e f -> k (a, b, c, d, e, f) forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d e f -> k (a, b, c, d, e, f) forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ \b c d e f -> k (a, b, c, d, e, f) forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d e f -> k (a, b, c, d, e, f) forSome [] k = forSome_ k -- 7 Tuple instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SymWord f, SymWord g, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) where forAll_ k = forall_ >>= \a -> forAll_ $ \b c d e f g -> k (a, b, c, d, e, f, g) forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d e f g -> k (a, b, c, d, e, f, g) forAll [] k = forAll_ k forSome_ k = exists_ >>= \a -> forSome_ $ \b c d e f g -> k (a, b, c, d, e, f, g) forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d e f g -> k (a, b, c, d, e, f, g) forSome [] k = forSome_ k -- | Run an arbitrary symbolic computation, equivalent to @'runSMTWith' 'defaultSMTCfg'@ runSMT :: Symbolic a -> IO a runSMT = runSMTWith defaultSMTCfg -- | Runs an arbitrary symbolic computation, exposed to the user in SAT mode runSMTWith :: SMTConfig -> Symbolic a -> IO a runSMTWith cfg a = fst <$> runSymbolic (SMTMode ISetup True cfg) a -- | Runs with a query. runWithQuery :: Provable a => Bool -> Query b -> SMTConfig -> a -> IO b runWithQuery isSAT q cfg a = fst <$> runSymbolic (SMTMode ISetup isSAT cfg) comp where comp = do _ <- (if isSAT then forSome_ else forAll_) a >>= output Control.query q -- | Check if a safe-call was safe or not, turning a 'SafeResult' to a Bool. isSafe :: SafeResult -> Bool isSafe (SafeResult (_, _, result)) = case result of Unsatisfiable{} -> True Satisfiable{} -> False SatExtField{} -> False -- conservative Unknown{} -> False -- conservative ProofError{} -> False -- conservative -- | Perform an action asynchronously, returning results together with diff-time. runInThread :: NFData b => UTCTime -> (SMTConfig -> IO b) -> SMTConfig -> IO (Async (Solver, NominalDiffTime, b)) runInThread beginTime action config = async $ do result <- action config endTime <- rnf result `seq` getCurrentTime return (name (solver config), endTime `diffUTCTime` beginTime, result) -- | Perform action for all given configs, return the first one that wins. Note that we do -- not wait for the other asyncs to terminate; hopefully they'll do so quickly. sbvWithAny :: NFData b => [SMTConfig] -> (SMTConfig -> a -> IO b) -> a -> IO (Solver, NominalDiffTime, b) sbvWithAny [] _ _ = error "SBV.withAny: No solvers given!" sbvWithAny solvers what a = do beginTime <- getCurrentTime snd `fmap` (mapM (runInThread beginTime (`what` a)) solvers >>= waitAnyFastCancel) where -- Async's `waitAnyCancel` nicely blocks; so we use this variant to ignore the -- wait part for killed threads. waitAnyFastCancel asyncs = waitAny asyncs `finally` mapM_ cancelFast asyncs cancelFast other = throwTo (asyncThreadId other) ThreadKilled -- | Perform action for all given configs, return all the results. sbvWithAll :: NFData b => [SMTConfig] -> (SMTConfig -> a -> IO b) -> a -> IO [(Solver, NominalDiffTime, b)] sbvWithAll solvers what a = do beginTime <- getCurrentTime mapM (runInThread beginTime (`what` a)) solvers >>= (unsafeInterleaveIO . go) where go [] = return [] go as = do (d, r) <- waitAny as -- The following filter works because the Eq instance on Async -- checks the thread-id; so we know that we're removing the -- correct solver from the list. This also allows for -- running the same-solver (with different options), since -- they will get different thread-ids. rs <- unsafeInterleaveIO $ go (filter (/= d) as) return (r : rs) -- | Symbolically executable program fragments. This class is mainly used for 'safe' calls, and is sufficently populated internally to cover most use -- cases. Users can extend it as they wish to allow 'safe' checks for SBV programs that return/take types that are user-defined. class SExecutable a where sName_ :: a -> Symbolic () sName :: [String] -> a -> Symbolic () -- | Check safety using the default solver. safe :: a -> IO [SafeResult] safe = safeWith defaultSMTCfg -- | Check if any of the 'sAssert' calls can be violated. safeWith :: SMTConfig -> a -> IO [SafeResult] safeWith cfg a = do cwd <- (++ "/") <$> getCurrentDirectory let mkRelative path | cwd `isPrefixOf` path = drop (length cwd) path | True = path fst <$> runSymbolic (SMTMode ISetup True cfg) (sName_ a >> check mkRelative) where check mkRelative = Control.query $ Control.getSBVAssertions >>= mapM (verify mkRelative) -- check that the cond is unsatisfiable. If satisfiable, that would -- indicate the assignment under which the 'sAssert' would fail verify :: (FilePath -> FilePath) -> (String, Maybe CallStack, SW) -> Query SafeResult verify mkRelative (msg, cs, cond) = do let locInfo ps = let loc (f, sl) = concat [mkRelative (srcLocFile sl), ":", show (srcLocStartLine sl), ":", show (srcLocStartCol sl), ":", f] in intercalate ",\n " (map loc ps) location = (locInfo . getCallStack) `fmap` cs result <- do Control.push 1 Control.send True $ "(assert " ++ show cond ++ ")" r <- Control.getSMTResult Control.pop 1 return r return $ SafeResult (location, msg, result) instance NFData a => SExecutable (Symbolic a) where sName_ a = a >>= \r -> rnf r `seq` return () sName [] = sName_ sName xs = error $ "SBV.SExecutable.sName: Extra unmapped name(s): " ++ intercalate ", " xs instance SExecutable (SBV a) where sName_ v = sName_ (output v) sName xs v = sName xs (output v) -- Unit output instance SExecutable () where sName_ () = sName_ (output ()) sName xs () = sName xs (output ()) -- List output instance SExecutable [SBV a] where sName_ vs = sName_ (output vs) sName xs vs = sName xs (output vs) -- 2 Tuple output instance (NFData a, SymWord a, NFData b, SymWord b) => SExecutable (SBV a, SBV b) where sName_ (a, b) = sName_ (output a >> output b) sName _ = sName_ -- 3 Tuple output instance (NFData a, SymWord a, NFData b, SymWord b, NFData c, SymWord c) => SExecutable (SBV a, SBV b, SBV c) where sName_ (a, b, c) = sName_ (output a >> output b >> output c) sName _ = sName_ -- 4 Tuple output instance (NFData a, SymWord a, NFData b, SymWord b, NFData c, SymWord c, NFData d, SymWord d) => SExecutable (SBV a, SBV b, SBV c, SBV d) where sName_ (a, b, c, d) = sName_ (output a >> output b >> output c >> output c >> output d) sName _ = sName_ -- 5 Tuple output instance (NFData a, SymWord a, NFData b, SymWord b, NFData c, SymWord c, NFData d, SymWord d, NFData e, SymWord e) => SExecutable (SBV a, SBV b, SBV c, SBV d, SBV e) where sName_ (a, b, c, d, e) = sName_ (output a >> output b >> output c >> output d >> output e) sName _ = sName_ -- 6 Tuple output instance (NFData a, SymWord a, NFData b, SymWord b, NFData c, SymWord c, NFData d, SymWord d, NFData e, SymWord e, NFData f, SymWord f) => SExecutable (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) where sName_ (a, b, c, d, e, f) = sName_ (output a >> output b >> output c >> output d >> output e >> output f) sName _ = sName_ -- 7 Tuple output instance (NFData a, SymWord a, NFData b, SymWord b, NFData c, SymWord c, NFData d, SymWord d, NFData e, SymWord e, NFData f, SymWord f, NFData g, SymWord g) => SExecutable (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) where sName_ (a, b, c, d, e, f, g) = sName_ (output a >> output b >> output c >> output d >> output e >> output f >> output g) sName _ = sName_ -- Functions instance (SymWord a, SExecutable p) => SExecutable (SBV a -> p) where sName_ k = exists_ >>= \a -> sName_ $ k a sName (s:ss) k = exists s >>= \a -> sName ss $ k a sName [] k = sName_ k -- 2 Tuple input instance (SymWord a, SymWord b, SExecutable p) => SExecutable ((SBV a, SBV b) -> p) where sName_ k = exists_ >>= \a -> sName_ $ \b -> k (a, b) sName (s:ss) k = exists s >>= \a -> sName ss $ \b -> k (a, b) sName [] k = sName_ k -- 3 Tuple input instance (SymWord a, SymWord b, SymWord c, SExecutable p) => SExecutable ((SBV a, SBV b, SBV c) -> p) where sName_ k = exists_ >>= \a -> sName_ $ \b c -> k (a, b, c) sName (s:ss) k = exists s >>= \a -> sName ss $ \b c -> k (a, b, c) sName [] k = sName_ k -- 4 Tuple input instance (SymWord a, SymWord b, SymWord c, SymWord d, SExecutable p) => SExecutable ((SBV a, SBV b, SBV c, SBV d) -> p) where sName_ k = exists_ >>= \a -> sName_ $ \b c d -> k (a, b, c, d) sName (s:ss) k = exists s >>= \a -> sName ss $ \b c d -> k (a, b, c, d) sName [] k = sName_ k -- 5 Tuple input instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SExecutable p) => SExecutable ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) where sName_ k = exists_ >>= \a -> sName_ $ \b c d e -> k (a, b, c, d, e) sName (s:ss) k = exists s >>= \a -> sName ss $ \b c d e -> k (a, b, c, d, e) sName [] k = sName_ k -- 6 Tuple input instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SymWord f, SExecutable p) => SExecutable ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) where sName_ k = exists_ >>= \a -> sName_ $ \b c d e f -> k (a, b, c, d, e, f) sName (s:ss) k = exists s >>= \a -> sName ss $ \b c d e f -> k (a, b, c, d, e, f) sName [] k = sName_ k -- 7 Tuple input instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SymWord f, SymWord g, SExecutable p) => SExecutable ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) where sName_ k = exists_ >>= \a -> sName_ $ \b c d e f g -> k (a, b, c, d, e, f, g) sName (s:ss) k = exists s >>= \a -> sName ss $ \b c d e f g -> k (a, b, c, d, e, f, g) sName [] k = sName_ k {-# ANN module ("HLint: ignore Reduce duplication" :: String) #-}